Answer:
The correct answer is (b) 1,280,000,000.
Step-by-step explanation:
Explanation:
For the area code, we have two choices for the second digit (0 or 1), and 8 choices for each of the first and third digits (since they cannot be 0 or 1). Therefore, there are 8 x 2 x 8 = 128 possible area codes.
For the seven-digit number, we have 8 choices for the first digit (since it cannot be 0 or 1), and 10 choices for each of the remaining 6 digits. Therefore, there are 8 x 10 x 10 x 10 x 10 x 10 x 10 = 8 x 10^6 possible seven-digit numbers.
To get the total number of possible phone numbers, we multiply the number of possible area codes by the number of possible seven-digit numbers:
128 x 8 x 10^6 = 1,280,000,000
Therefore, there are 1,280,000,000 possible phone numbers that satisfy the given conditions.
20.) Lines m and n cross to form Z1, 22, 23, and 24, where m 1 = 50. Z1 and /4 are supplementary. m L
m <4. What is m /2?
The measure of m∠2 is given as 130
How to solve for the angleSince ∠1 and ∠4 are supplementary, their sum equals 180°:
m∠4 = 180° - m∠1
m∠4 = 180° - 50°
m∠4 = 130°
Now, we need to find m∠2. Since lines m and n cross, forming vertical angles, m∠1 is vertical to m∠3 and m∠2 is vertical to m∠4. Vertical angles are equal, so:
m∠2 = m∠4
m∠2 = 130°
Thus, m∠2 is 130°.
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At dinner, Mr. and Mrs. Smith decided to leave a 20% tip for their server. Their meal cost $63.20 (before the tip). What is their change if they gave the server $80.00?
Answer: $4.16
Step-by-step explanation:
20% of 63.20 = 12.64
63.20 + 12.64 = 75.84
80.00 - 75.84 = 4.16
Please can you explain the answer:
I got
1/2n^2 +n^2 - 7/2
but it says this is wrong
Answer:
an = 1/2n² -1/2n -2
Step-by-step explanation:
You want a formula for the n-th term of the quadratic sequence -2, -1, 1, 4.
Linear equationsUsing x = 1, 2, 3 and y = -2, -1, 1 we can write equations for the coefficients a, b, c of the quadratic expression ax² +bx +c.
a(1²) +b(1) +c = -2
a(2²) +b(2) +c = -1
a(3²) +b(3) +c = 1
SolutionSubtracting the first equation from the other two, we get ...
3a +b = 1
8a +2b = 3
Subtracting twice the first from the second of these, we get ...
(8a +2b) -2(3a +b) = (3) -2(1)
2a = 1
a = 1/2
Then b can be found from ...
b = 1 -3a = 1 - 3/2 = -1/2
And c can be found from ...
-2 -b -a = c = -2 -(-1/2) -(1/2) = -2
The formula is ...
an = 1/2n² -1/2n -2
__
Additional comment
For systems of equations, the solver used in the second attachment works well. It tells us (a, b, c) = (1/2, -1/2, -2) as we found above.
Alternate solution
The first differences of the given terms are ...
1, 2, 3
And their differences are ...
1, 1
The coefficient of n² is half this second-difference value: 1/2.
If you subtract 1/2n² from the given terms, you get ...
-5/2, -3, -7/2, -4
This arithmetic sequence has the formula ...
a1 +d(n -1)
-5/2 +(-1/2)(n -1) = -1/2n -2
Adding this to the term we subtracted gives ...
an = 1/2n² -1/2n -2 . . . . . as above
A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour in order to score as many points as possible. The sample yielded an average score of 375 and a standard deviation of 100. The resulting 90% confidence interval is 375 +31. Which of the following statements best summarizes the meaning of this confidence interval? If we repeated this procedure many times, about 10% of the confidence intervals constructed will fail to include the mean number of points scored by all students at a high school. If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time. o Approximately 10% of all students at the high school will score more than 406 points. Approximately 90% of the students at a high school will have an average score between 344 and 406 points.
If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.
This means that we are 90% confident that the true population mean of points scored by all students at the high school falls within this range based on the sample of 30 students who played the game for an hour.
A random sample of 30 students at a high school was allowed to play a popular cell phone game for an hour, yielding an average score of 375 with a standard deviation of 100. The 90% confidence interval is 375 ± 31. The statement that best summarizes the meaning of this confidence interval is: If we repeated this procedure many times, the average number of points scored by our sample of 30 students will be between 344 and 406 points approximately 90% of the time.
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answer the statistical measures and create a box and whiskers plot for the following set of data
The statistical measures are: Min: 6 Q1: 7 Med: 11.5 Q3: 13 Max: 15.
The box and whiskers plot is given below.
How to Create a Box and Whiskers Plot?To create a box and whiskers plot, we have to first derive the statistical measures of the data set given, which is the five number summary that include, the mina nd max values, the median, and the quartiles.
Given the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, the five number summary which are the statistical measures are:
Minimum: 6 (lowest value)
First Quartile: 7 (middle of the first half of the data)
Median: 11.5 (center of the data set)
Third Quartile: 13 (middle of the second half of the data)
Maximum: 15 (largest value).
The box and whiskers plot of the data set, 6, 7, 7, 8, 10, 13, 13, 13, 15, 15, is shown in the diagram attached below.
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your friend deposits $6500 in an investment account that earns 8.4% annual interest. Find the balance after 12 years when the interest is compounded monthly.
Answer:
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where:
A = the balance after t years
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this problem, P = $6,500, r = 0.084, n = 12 (monthly compounding), and t = 12. Plugging in these values, we get:
A = $6,500(1 + 0.084/12)^(12*12)
A = $6,500(1.007)^144
A = $6,500(2.008)
A = $13,052.20
Therefore, the balance after 12 years is $13,052.20 when the interest is compounded monthly.
HELP ASAP PLEASE!!! I need help
Answer:
5.6 miles
Second answer option
Step-by-step explanation:
From the tables we see that 1 mile ≈ 1.61 km
Therefore 1 km ≈ 1/1.61 mile
9 km ≈ 9 x 1/1.61 ≈ 9/1.61 ≈ 5.592341 miles
Rounded to first decimal(tenth) that would be 5.6 miles
This is the second answer option
A lighthouse casts a shadow that is 18 yards long. At the same time, a nearby house that is 9 yards tall casts a shadow that is 6 yards long. What is the height of the lighthouse?
The calculated height of the lighthouse, h will be yards
What will be the height of the lighthouseFrom the question, we have the following parameters that can be used in our computation:
Similar triangles of shadows and house
This means that
Ratio = Division or ratio of corresponding sides
So, we have
h : 9 = 18 : 6
So, we have the following representation
h/9 = 18/6
This gives
h = 9 * 18/6
By calculation, we have
height = 27 yards
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HELP PLEASE
A random sample of 100 customers at a local ice cream shop were asked what their favorite topping was. The following data was collected from the customers.
Topping Sprinkles Nuts Hot Fudge Chocolate Chips
Number of Customers 17 12 27 44
Which of the following graphs correctly displays the data?
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44
a bar graph titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27 ,and the fourth bar labeled chocolate chips going to a value of 44
a histogram titled favorite topping with the x axis labeled topping and the y axis labeled number of customers, with the first bar labeled nuts going to a value of 17, the second bar labeled sprinkles going to a value of 12, the third bar labeled chocolate chips going to a value of 27, and the fourth bar labeled hot fudge going to a value of 44
Option a. The graph that would correctly display the data that we have jere would be: a bar graph titled favorite topping with the x-axis labeled topping and the y-axis labeled number of customers, with the first bar labeled sprinkles going to a value of 17, the second bar labeled nuts going to a value of 12, the third bar labeled hot fudge going to a value of 27, and the fourth bar labeled chocolate chips going to a value of 44.
How to determine the correct graphThe correct graph to display this type of categorical data is a bar graph. The correct option should show the data with the correct number of customers for each topping as it is listed in the question we have :
Sprinkles: 17
Nuts: 12
Hot Fudge: 27
Chocolate Chips: 44
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how many constant terms are in n²÷3+6n
Answer:
3
Step-by-step explanation:
9.5 in. 2 in. 9.5 in. 2 in.
What's the area?
Answer:
it is 19 brainliest please
Step-by-step explanation:
a data analyst performs a correlation analysis between two quantities. the result of the analysis is an r value of 0. what does this mean?
An r value of 0 in a correlation analysis indicates that there is no linear relationship between the two quantities being analyzed.
This means that there is no correlation between the two variables, and any observed pattern or association between them is likely due to chance. In other words, the values of one variable do not predict the values of the other variable. However, it is important to note that a correlation analysis only measures linear relationships, and there may still be other types of relationships between the variables that are not captured by the r value.
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Suppose y varies directly with x. When x is 7, y is 28. What is y when x is 13?
Therefore, when x is 13, y is 52 if y varies directly with x.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It is usually written using an equal sign (=). Equations can contain variables, which are usually represented by letters, and the goal is often to solve the equation for the value(s) of the variable(s) that make the equation true.
Here,
If y varies directly with x, then we can write the relationship between y and x using the equation:
y = kx
where k is the constant of proportionality. To solve for k, we can use the given information that when x is 7, y is 28:
28 = k(7)
Solving for k, we get:
k = 4
Now that we know k, we can use the equation to find y when x is 13:
y = 4(13)
y = 52
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Janice is searching for a cellular phone plan. The table shows information about monthly
prices for two different cellular phone plans.
Cellular Phone Plan
Digital Talk
Cell-to-Cell
Cost Description
Variable rate: $0.20 per minute
Fixed rate: $50 per month
Janice has a coupon for 25% off the fixed cost per month for the first year of service with
Cell-to-Cell. What will the discounted cost be for an entire year of service with Cell-to-Cell?
The discounted cost for an entire year of service with cell-to-cell would be = $450
How to calculate the discounted cost for cell-to-cell services?The fixed rate for cell-to-cell services for a month = $50
Therefore the cost for a year would be = 50×12 = $600
The percentage of discount on the coupon = 25%of cost Price.
That is 25% of 600
= 25/100 × 600/1
= 25×6
= $150
Therefore, the discounted cost for an entire year of service with cell-to-cell would be = 600-150=$450
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Right 804, 082 and expanded form two different ways
Expanded form of 804082 is 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1.
To write the number 804082 in expanded form, we need to break it down into its component parts based on place value.
Expanded form 1:
804082 = 8 x 100000 + 0 x 10000 + 4 x 1000 + 0 x 100 + 8 x 10 + 2 x 1
In this expanded form, we can see that the digit 8 is in the hundred thousands place, the digit 0 is in the ten thousands place, the digit 4 is in the thousands place, the digit 0 is in the hundreds place, the digit 8 is in the tens place, and the digit 2 is in the ones place.
Expanded form 2:
804082 = 8 x [tex]10^{5}[/tex] + 0 x [tex]10^{4}[/tex] + 4 x [tex]10^{3}[/tex] + 0 x [tex]10^{2}[/tex] + 8 x [tex]10^{1}[/tex] + 2 x [tex]10^{0}[/tex]
In this expanded form, we can see that each digit in the number is multiplied by its corresponding power of 10 based on its position in the number.
Both forms give us the same result, but they express the number in different ways based on the place value of each digit.
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A line has a slope of -5 and a y-intercept
of 4
Write its equation in slope-intercept
form.
Write your answer using integers, proper
fractions, and improper fractions in
simplest form.
Answer:
y = -5x + 4.
Step-by-step explanation:
Slope-intercept formula: y = mx (m is slope) + B (y-intercept)
Plug in it:
y = 5x + 4.
a 30 gram sample of a substance that's used to sterilize surgical instruments has a k value of 0.1253 find the substance's half life in days round your answer to the nearest tenth
When, a 30 gram sample of a substance that's used to sterilize surgical instruments has a k value of 0.1253. Then, the half-life of the substance is 8.0 days.
The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay. The decay of the substance can be modeled using the formula;
N = N0 × [tex]2^{(-kt)}[/tex]
where N is the amount of substance at time t, N0 is the initial amount of substance, k is the decay constant, and t is the time.
In this case, we know that the initial amount of the substance is 30 grams, and the decay constant (k value) is 0.1253. We want to find the half-life, which we can denote as [tex]t_{1/2}[/tex]
When half of the initial amount of substance remains, the amount of substance is [tex]N_{0}[/tex]/2. So we can substitute N = [tex]N_{0}[/tex]/2 and solve for [tex]t_{1/2}[/tex];
N = [tex]N_{0}[/tex]/2
[tex]N_{0}[/tex]/2 = [tex]N_{0}[/tex] × [tex]2^{(-kt1/2)}[/tex]
1/2 = [tex]2^{(-kt1/2)}[/tex]
log2(1/2) = log2([tex]2^{(-kt1/2)}[/tex])
-1 = [tex]-kt_{1/2}[/tex]
[tex]t_{1/2}[/tex] = 1/k × log2(2)
[tex]t_{1/2}[/tex] = 1/k
Substituting the given value of k, we get:
[tex]t_{1/2}[/tex] = 1/0.1253
[tex]t_{1/2}[/tex] ≈ 7.9816
Therefore, the half-life of the substance is approximately 8.0 days.
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A water sample shows 0.034 grams of some trace element for every cubic centimeter of water. Abdoulaye uses a container in the shape of a right cylinder with a diameter of 13.4 cm and a height of 10.3 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Abdoulaye collected? Round your answer to the nearest tenth.
Answer:49.4g
Step-by-step explanation:
After considering the given data we conclude that the total amount of trace element collected by Abdoulaye is 4 grams.
Formula for volume of a cylinder
[tex]V = \pi r^2 h[/tex]
Here,
Radius = 13.4 / 2 = 6.7 cm
Height = 10.3
Then
V = 3.14 × (6.7)² × 10.3
V = 1,451.8 cubic centimeters
Volume of cylinder is approximately 1,451.8 cubic centimeters.
In the event a water sample shows 0.034 grams of some trace element for every cubic centimeter of water, then the amount of trace element in the sample can be evaluated by multiplying the volume of the sample by the concentration of the trace element in the water sample.
1.451.8 × 0.034 = 49.36 grams
Then , approximately 49.36 grams of trace element has Abdoulaye collected rounding the value to the nearest tenth which is 4 grams.
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An empty shipping box has a mass of. 3 pounds. A clothing store
The maximum weight of clothes that can be shipped in the box without exceeding the weight limit for shipping is 47 pounds.
To determine the maximum weight of clothes that can be shipped in the box, we first need to know the weight limit for shipping. This will vary depending on the shipping method and destination. Let's assume that the weight limit for shipping is 50 pounds.
We subtract the weight of the empty box from the weight limit for shipping: 50 pounds - 3 pounds = 47 pounds.
It is always a good idea to check the specific weight limit for the shipping method and destination before packing and shipping any items to avoid any issues or additional fees.
The complete question is:
What is the maximum weight of clothes that can be shipped in the box without exceeding the weight limit for shipping?
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Frank sells lemonade in 500ml bottles, 6 bottles per carton, 4 cartons per case, and 96 cases per bakkie. How many litres of lemonade can he transport on a fully loaded bakkie?
Answer: yes he can transport them all
Step-by-step explanation: yes.
Please help me with this questions , I think that they are not really hard , but I don’t know how to do them
The percentage of values and the z-scores are listed below
Calculating the percentage of valuesHere, we have
Between z = 0.53 and 2.67
This is represented as
Percentage = (0.53 < z < 2.67)
Using a graphing calculator, we have
Percentage = 29.43%
Next, we have
To the right of z = 1.61
This is represented as
Percentage = x > 1.61
Using a graphing calculator, we have
Percentage = 5.40%
Calculating the z-scoresHere, we have
Percentage = 35% to the left of the z-score
This means that
P(z < z) = 0.35
Using a graphing calculator, we have
z = -0.385
Next, we have
Percentage = 18% to the right of the z-score
This means that
P(z > z) = 0.18
Using a graphing calculator, we have
z = 0.915
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A local company makes two types of soups, chicken and beef barley. Each batch of chicken soup takes 3 hours to prepare and 4 hours to package. Each batch of beef barley takes 3.5 hours to prepare but only 2 hours to package. There are 5 preparation workers and 6 packaging workers in the company. Each of them works 40 hours per week.
Part A:
Create a system of two inequalities that relates the number of batches of chicken soup, c, and the number of batches of beef barley soup, b, that can be made by the 5 preparation workers and the 6 packaging workers each week. Assume c≥0 and b≥0.
Part B:
Give two possible combinations of batches of chicken soup and beef barley soup that could be made in one week based on the constraints?
Answer:
Step-by-step explanation:
Part A:
Let's use the information given in the problem to create the inequalities:
Each batch of chicken soup takes 3 hours to prepare, so the total preparation time for c batches of chicken soup is 3c hours.
Each batch of beef barley takes 3.5 hours to prepare, so the total preparation time for b batches of beef barley soup is 3.5b hours.
Each batch of chicken soup takes 4 hours to package, so the total packaging time for c batches of chicken soup is 4c hours.
Each batch of beef barley takes 2 hours to package, so the total packaging time for b batches of beef barley soup is 2b hours.
There are 5 preparation workers who work 40 hours per week, so the total preparation time available is 5 workers x 40 hours/worker = 200 hours.
There are 6 packaging workers who work 40 hours per week, so the total packaging time available is 6 workers x 40 hours/worker = 240 hours.
To create the system of inequalities, we need to make sure that the total preparation and packaging times for both types of soup do not exceed the available time. Therefore:
3c + 3.5b ≤ 200 (total preparation time ≤ available preparation time)
4c + 2b ≤ 240 (total packaging time ≤ available packaging time)
Also, we have the non-negativity constraints:
c ≥ 0 (number of batches of chicken soup is non-negative)
b ≥ 0 (number of batches of beef barley soup is non-negative)
Therefore, the system of inequalities is:
3c + 3.5b ≤ 200
4c + 2b ≤ 240
c ≥ 0
b ≥ 0
Part B:
To find two possible combinations of batches of chicken soup and beef barley soup that could be made in one week based on the constraints, we can try different values for c and b that satisfy the inequalities from Part A. Here are two possible combinations:
Combination 1: c = 40, b = 0
Total preparation time: 3c + 3.5b = 3(40) + 3.5(0) = 120
Total packaging time: 4c + 2b = 4(40) + 2(0) = 160
Both inequalities are satisfied, and c and b are non-negative.
Therefore, in one week, the company can make 40 batches of chicken soup and 0 batches of beef barley soup.
Combination 2: c = 30, b = 20
Total preparation time: 3c + 3.5b = 3(30) + 3.5(20) = 135
Total packaging time: 4c + 2b = 4(30) + 2(20) = 160
Both inequalities are satisfied, and c and b are non-negative.
Therefore, in one week, the company can make 30 batches of chicken soup and 20 batches of beef barley soup.
Solve negative a minus six sevenths equals two thirds for a.
a equals negative 32 over 21
a equals 32 over 21
a equals negative 8 over 21
a equals 8 over 21
excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 36 kmph. for how many minutes does the bus stop per hour?
When excluding stoppages, the speed of a bus is 54 km/h, and including stoppages, it is 36 km/h. the bus stop is 20 minutes per hour
We have to Calculate the distance traveled by bus in 1 hour excluding stoppages and calculate the distance traveled by bus in 1 hour including stoppages. Then we have to calculate the time taken to cover that difference between the distances and convert the calculated time into minutes.
Given data:
The speed of a bus while excluding stoppages = 54 km/h.
the speed of the bus while including stoppages = 36 km/hr.
From the given data we can say that:
The Distance traveled by bus in 1 hour, excluding stoppages is = 54 km.
The Distance traveled by bus in 1 hour, including stoppages, is = 36 km.
Distance traveled = Distance traveled by bus in 1 hour excluding stoppages – distance traveled by bus in 1 hour including stoppages
= 54km − 36km = 18km
The bus covers 18 km less due to stoppages.
the time taken to cover18 km, = distance traveled / speed of the bus
= 18km / 54km/hour
= 1 / 3 hour
Time taken in minutes = ( 1 / 3×60 )minutes
=20minutes
Therefore, the bus stops per hour for 20 minutes.
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the u.s. senate of the 109th congress consisted of 55 republicans, 44 democrats, and 1 independent. how many committees can be formed if each committee must have 4 republicans and 3 democrats?
4,516,932,420 committees can be formed if each committee must have 4 republicans and 3 democrats
We have,
Republicans= 55
Democrats = 44
Independent= 1
Using Combination, the number of committees can be formed
= C(55, 4) / C(44, 3)
= 55! / 4! (55-4)! ÷ 44!/ 3! (44-3)!
= 55! / 4! 51! x 44! / 3! 41!
= 55 x 54 x 53 x 52 x 44 x 43 x 42/ 4 x 3 x 2 x 3 x 2
= 650,438,268,480 / 144
= 4,516,932,420
Thus, there are 4,516,932,420 committees can be formed.
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I need some help with this.
Answer: 23
Step-by-step explanation:
The range of the data set is the same thing as subtracting the smallest value from the largest value.
Here, our smallest value is 8 and our largest value is 31.
31 - 8 = 23
This data set has a range of 23.
One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 3 units wide.
Answer: 84 square inches.
Step-by-step explanation:
Side A of shaded: 5+3+3 = 11
Side B of shaded: 3+3+3= 9
11x9= 99
99-(3x5{normal rectangle area})= 84
Circle O has a circumference of 3677 cm.
What is the length of the radius ?
6 cm
18 cm
36 cm
72 cm
Answer:
585.14
Step-by-step explanation:
3677=2πr
r=3677÷44/7
=585.14
a fair die is rolled times. what is the probability that a is obtained on at least one of the rolls? round your answer to three decimal places.
The probability that a 6 is obtained on at least one of the rolls is 67%.
The probability of getting a 6 on one roll of a fair die is 1/6. The probability of not getting a 6 on one roll is 5/6.
Let's use the complementary probability approach to calculate the probability of getting no 6 on any of the 5 rolls. The probability of not getting a 6 on one roll is 5/6, so the probability of not getting a 6 on all 5 rolls is (5/6)^5 ≈ 0.327.
Therefore, the probability of getting at least one 6 on 5 rolls is 1 - 0.327 ≈ 0.673.
So the probability of getting at least one 6 on 5 rolls of a fair die is approximately 0.673, or 67.3% when rounded to three decimal places. This means that if you roll a fair die 5 times, you have about a 67% chance of getting at least one 6.
Correct Question :
A fair die is rolled 5 times. What is the probability that a 6 is obtained on at least one of the rolls? Round your answer to three decimal places.
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question 16
Estimate the sum by rounding each number to the nearest half or whole.
4 1/2 + 2 7/12
A. 6 1/2
B. 7
C. 7 1/2
D. 6
Answer:
The answer to your problem is, 12 1/2
Step-by-step explanation:
As shown to the problem we would need to add
4 1/2 + 2 7/12
Lets make them equivalent denominators:
1/2 & 7/12
= 24
1/2 = 12/24
7/12 = 14/24
Then make the new problem into;
4 12/24 + 7 14/24
= 12 1/2
Thus the answer to your problem is, 12 1/2
